TIL that the fine-structure constant, a dimensionless quantity roughly equal to 1/137, is one of nature's most important numbers. While this constant has now been determined to many decimal places, it is used to characterize the strength of the electromagnetic force affecting charged particles. quantamagazine.org/physic…
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A Question about the Spatial-Dimensionless Nature of a Singularity

Our current understanding of Black Holes dictates that all the matter that falls into a black hole is condensed into a dimensionless shape - a singularity/ringularity (a structure lacking measurement in the Three Spatial Dimensions, only having mass, spin, and electric charge).

But let's explore this for a moment; we are incapable of observing any details beyond the event horizon due to the inability of photon emissions to escape. Therefore, we have no firm conclusion about what we would find behind it. The event horizon (while only being a Two-Dimensional Surface Area) does encompass a Three-Dimensional Volume that is capable of growing as more matter is consumed and compressed within. Couldn't it, therefore, be possible that all the matter and energy is just compressed enough to be enclosed behind this volume, and a Black Hole is simply produced when matter is compressed beyond a certain point?

If an event horizon encloses a positive volume of X, would it be possible, therefore, that all the matter within the black hole could still occupy a volume of X-Y, where Y is a positive value less than X? Could a black hole exist where all the matter is compressed just enough to hide it without it being infinitely small?

Since we cannot take observations in the Electromagnetic Spectrum, it would seem mathematically sound to continue treating a black hole as a dimensionless point in space-time within our equations and proofs, but would it be prudent to include a note/asterisk when discussing anything that lays beyond the event horizon, as we simply don't know?

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Post-posting Thoughts:
- Compressing matter beyond an event horizon any further doesn't seem likely to change the boundary of the black hole- that can only be affected by adding more matter to the black hole...
- Compression of matter causes spin to increase; therefore, infinite compression (thus resulting in a dimensionless object) would produce infinite spin(?). But Black Holes have a measureable spin noticeable by shifts in their magnetic field(?)

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Reis, Jaime (b.1983): Fluxus, Dimensionless Sound (B) (2012-17) for flute and electronics youtube.com/watch?v=bwhD_…
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Perfect Yin Yang can be constructed with a fractal seed of life, which also encodes a 1/64 dimensionless scalar ratio. The basic building block of mass is a planck spherical unit, which itself made up of 64 perfectly packed spheres (the flower of life).
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Proof that Archimedes number is indeed dimensionless

So I have an assignment to prove that Archimedes number is dimensionless , but each time I try I’m left with m^3/kg. Help would be great.

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πŸ‘€︎ u/noneskillz
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ELI5: Dimensionless Physical Quantities

I've done my fair share of reading and seem to still lack some basic understanding that is inhibiting me from grasping why pi or e are dimensionless. Does this have to do with SI or is something dimensionless because it lacks previous or subsequent quantities?

Thanks!

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Time variation of a fundamental dimensionless constant arxiv.org/pdf/0903.5321.p…
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If both sides of an equation are dimensionless, is the equation dimensionally correct?

Title says it all

I hope no one calls me retarded for asking this question.

I was and am preparing for JEE exams ( I am from India) and there was a question in the book i was solving saying if the equations are dimensionally correct and both sides of equations were dimensionless so will it be dimensionally correct?

Ignore English FFS.

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PSA: It’s non-dimensional or dimensionless, you can’t say we’re making it non-dimensionless.

That is all.

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πŸ‘€︎ u/Miscbrah97
πŸ“…︎ Nov 06 2020
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No Jack, they're dimensionless.
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πŸ“…︎ Sep 18 2020
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Looking at NACA paper, CL seems to be using this unit. I thought CL is dimensionless
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πŸ“…︎ Aug 09 2020
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looking for books and videos/ documentaries on energy work, 5th dimensionless.

hello everyone! I have this half built concept about life and i was hoping to find more resources on it! so i believe at we come to this earth to find our souls purpose and until we reach the 5th dimension we are reincarnated, but once we reach the 5th dimensions we are able to ascended to the ether. so anyway books are info on that topic would be wonderful!

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πŸ‘€︎ u/Shae_dehlia
πŸ“…︎ Dec 10 2020
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The Q Factor, Dimensionless TDSE, Buckingham pi theorem, and much more
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πŸ‘€︎ u/sjyolo9011
πŸ“…︎ Dec 03 2020
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Standardized statistics are dimensionless, but measured in standard deviation units?

Intro stats textbooks frequently state that standardized statistics (e.g., z-statistic, t-statistic) are dimensionless. Rudimentary dimensional analysis proves this; the units cancel. But textbooks then go on to claim standardized statistics are measured in standard deviation units. My common sense tells me that, by definition, a dimensionless quantity has no units. So why the standard deviation units?

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Data Lake cheap, dimensionless and low resistance design arekusandr.medium.com/dat…
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πŸ“…︎ Nov 19 2020
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Question about making S.E. "dimensionless" in 1-D potential problems (V(x) = V0*sech^2(x/a) in this case)

Here is a LaTex image with the question so the equations aren't a pain in the *** to read.

Apparently this is a general rule-of-thumb-strategy to solve 1-D problems. The potential is a sech^2 and according to the professor one way of approaching this problem, which apparently can be extended pretty well to other problems, is to make the equation "dimensionless", that is, have every variable in the equation have no units.

I can get behind that idea, however, I am struggling to understand how some of the equations end up dimensionless (eqn 3)and how come he can (and what is the logic behind, or say, the clear motivation) define them that way. I would love to ask the professor but he...kinda never answers the question.

Thanks in advance!

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πŸ“…︎ Oct 03 2020
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Does anyone know good reliable comps for the new dimensionless heroes?

I really like ainz and he is so fucking strong imo. I was wondering how can we get the maximum benefit off of his skill set I mean does he work with eironn better or gwyneth ? And also what are your opinions I’d really like to know !

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GGD DEMO by Dimensionless | DIMENSION X soundcloud.com/bassfed/gg…
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The Cassandra Ratio, The Dimensionless Quantity Connecting Sun-Like Stars to Red Dwarfs on Mass-Radii Diagram
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πŸ“…︎ Sep 24 2020
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Data Lake cheap, dimensionless and low resistance design arekusandr.medium.com/dat…
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πŸ“…︎ Nov 19 2020
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No Jack, they're dimensionless.
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One day I would like to create a catalog of dimensionless spaces.
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πŸ‘€︎ u/shagminer
πŸ“…︎ Jul 29 2020
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Looking at NACA paper, CL seems to be using this unit. I thought CL is dimensionless
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Digital Divine - Dimensionless Life form youtube.com/watch?v=oeQvP…
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πŸ“…︎ Aug 28 2020
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Time variation of a fundamental dimensionless constant (aka. The best paper ever written)

https://arxiv.org/pdf/0903.5321.pdf

I known it's bit off topic, but I think you guys might like it.

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πŸ‘€︎ u/AWarhol
πŸ“…︎ Mar 01 2020
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Dimensionless number for acceleration?

I'm looking for a dimensionless number relating compressibility and acceleration. Just looking at the list on Wikipedia, Mach number send to be the only one related to compressibility and the ones related to acceleration are for gravity. Does anyone know if such a parameter exists? I think something like sqrt(2aL)/c might be a starting point.

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πŸ‘€︎ u/IBelieveInLogic
πŸ“…︎ May 06 2020
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I was a dimensionless cyborg for 37 seconds and still find it difficult to talk about it.
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πŸ‘€︎ u/shagminer
πŸ“…︎ Jul 23 2020
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Perfect Yin Yang can be constructed with a fractal seed of life, which also encodes a 1/64 dimensionless scalar ratio. The basic building block of mass is a planck spherical unit, which itself made up of 64 perfectly packed spheres (the flower of life).
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πŸ‘€︎ u/d8_thc
πŸ“…︎ Jan 07 2020
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Error in implementing a new solver: Argument of trancendental function not dimensionless

I have been trying to implement a scalar variance model in OpenFOAM recently (specifically the Abe-Kondoh-Nagano (1995) model). Unfortunately, I am running into the error as mentioned in the title.

I have checked and it appears that the fields should be dimensionless but for some reason, I still get the error. Here is how the field and function are defined:

const volScalarField& Rt = sqr(k)/(nu*epsilon);

const volScalarField fe ( exp(pow(Rt/6.5,2)) );

As can be seen, Rt should be dimensionless but the exp function within the fe definition complains it is not. I have checked the initial condition files where k, nu and epsilon are defined and the units are as they are supposed to be.

Could anyone help me with addressing this error or how I can print/ check what the dimensions of Rt are if not dimensionless. Thanks.

Edit: I am using OpenFOAM v7 for reference.

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πŸ“…︎ Jun 16 2020
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Is it possible to find dimensionless slope with only mean depth and mean width? Also, is Cross-sectional velocity the same as shear velocity?

Just like it says, is it possible and are those two the same? I'm trying to solve a salinity problem and first I need to find shear velocity, and to do that it's either the cross-sectional velocity or I need to find the dimensionless slope.

The help if appreciated.

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πŸ“°︎ r/FluidMechanics
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πŸ‘€︎ u/Smellstrom
πŸ“…︎ May 01 2020
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Dimensionless Deity
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πŸ“…︎ Dec 07 2019
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Why aren't clothing sizes simply in centimeters or inches? Why have arbitrary dimensionless numbers?
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πŸ“…︎ Apr 05 2020
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NEW DISCOVERY: THE MASTER KEY πŸ”‘ to the dimensionless Mathematical Constants. All relationships geometrically revealed by converting values between Compass Sexagesimal to Decimal and vice versa. by: Robert Edward Grant
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Døń’kΓΆth, the Dimensionless
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πŸ“…︎ Dec 19 2019
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Does anyone have the Dimensionless skin from the Space case as a wallpaper...

...or a wallpaper that looks like it?

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πŸ‘€︎ u/Something160
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